Graphing reciprocals of quadratic functions

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Now Playing:Graphing reciprocals of quadratic functions– Example 1
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  1. Given that f(x)=x29f(x)=x^2-9 , graph the reciprocal of the function f(x)f(x)
    Graphing reciprocals of linear functions
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    Notes
    We have learnt the basics of reciprocal functions. In this section, we will learn how to graph the reciprocal of a quadratic function, while applying the same principles we used when graphing the reciprocal of a linear function, while following the "6-steps Approach" noted below.
    Steps to graph the reciprocal of a function:
    1) Plot a horizontal asymptote
    at
    y=0y=0
    2) Plot vertical asymptote(s)
    equate the original function to 0; solve for xx
    3) Plot y-intercept(s)
    1y-intercept(s) of the original function\frac{1}{\text {y-intercept(s) of the original function}}
    4) Plot invariant points:
    equate the original function to +1 and -1; solve for xx
    5) Plot
    1vertex of the original function\frac{1}{\text {vertex of the original function}}
    6) Place your pen at the invariant points, then smoothly move away while tracing along the asymptotes!